Visiting the headquarters of the FBI in Washington on May 13, David Cameron inspected the Strategic Information and Operations Center, a fifth-floor suite of offices established, as a helpful official explained, to facilitate “the ability to manage several crises simultaneously.” That ability is being tested to the limit in the British Prime Minister, who is feverishly searching for solutions to a clutch of crises.

He started a three-day trip to the U.S. at the J. Edgar Hoover Building to discuss the lessons British and U.S. counterterrorism experts might draw from the Boston bombings. Later the same morning, he huddled with President Obama to brainstorm on a range of knotty issues, from the conflicts of the Middle East to stuttering global growth. He used the high visibility of the White House podium to announce the doubling of the U.K.’s nonmilitary aid to the Syrian opposition and to pump up hopes that Russia might leverage its influence to ease out the Assad regime. (On the eve of his American tour, Cameron made a 3,820-mile round trip from London to Sochi, on the Black Sea, in less than a day to take his charm offensive direct to Russian President Vladimir Putin.) In whatever down time remains, he has also been working the phones to build consensus ahead of the G-8 summit he will host in Northern Ireland next month.

Yet however far into the distance Cameron seems to gaze, no matter where he roams, his primary focus remains back home in Westminster and on Britain and its relationship with the European Union. Members of his own party have once again erupted into brawling over the subject that torpedoed Britain’s last Conservative government, ushering in an unbroken stretch of Labour rule from Tony Blair’s decisive first victory in 1997 to the elections in 2010 that failed to give Cameron an overall majority. That failure delivered his Conservatives into coalition with the Liberal Democrats, ardent Europhiles who have watched with mounting horror as Cameron has moved from insisting Britain’s future lies in Europe to promising an in-out referendum on E.U. membership, to be held after the next elections, due in 2015 — if the coalition holds together that long.

The promise, made in January, opened fresh rifts with the Lib Dems and only temporarily eased pressure from Tory Euroskeptics. Their party’s poor performance in local elections earlier this month after a surge in support for their Euroskeptic rivals, the UK Independence Party (UKIP), reminded Conservatives that promises are cheap. Unless Cameron wins — and wins a majority — he can’t deliver the referendum.

So backbench insurgents agitated for Cameron to enshrine his referendum promise in legislation before the election. They were angered to discover no mention of such a bill when Queen Elizabeth on May 8 read out her government’s plans for the new session of Parliament. And so, ignoring the first rule of politics — that no party that devotes more energy to fighting itself than fighting elections wins elections — they proposed a motion condemning the government’s omission. Cameron boarded a charter jet for the U.S. — as it happens, a jet owned and operated by Greeks, in the true spirit of the E.U. — knowing the messy, damaging vote was likely to take place in his absence.

As he stood next to Obama during their joint May 13 press conference and listened to the President give long, defensive answers to questions about the IRS imbroglio and Benghazi, Cameron may have taken some comfort. Misery loves company, as Britons say. The wearier Obama looked — and he looked dog tired — the perkier the British Premier seemed by comparison.

There was another reason for his inner glow. Before Cameron’s jet left Washington for his current destination, Boston, his aides revealed to journalists accompanying the Prime Minister that he has decided to back a so-called private member’s bill, a nongovernmental legislative draft, to be unveiled tomorrow, aimed at anchoring in law the promise for an E.U. referendum by the end of 2017.

If the Lib Dems or the Labour opposition vote the bill down, which they probably will, they’ll be accused of denying the British people a say on one of the most important questions facing the country. If the bill passes, it might help to burst the UKIP bubble. It’s tactical masterstroke, if strategically risky. The risk lies in the possibility, indeed the probability, that Britons given a say in the matter really would vote Britain out of Europe. Cameron still insists that British national interest is to remain in the E.U., part of the single market and part of the decisionmaking process, even if he wishes to redefine the terms of British membership.

In this vision and, underscoring that point, in his push for an E.U.-U.S. trade deal as part of Britain’s G-8 presidency, he gained support from Obama that will be factored into the debate back in Britain. “You probably want to see if you can fix what’s broken in a very important relationship before you break it off,” the President said, responding to question about the prospect of a U.K. exit from the E.U.

As Cameron continues his perambulations around the U.S., glad-handing influential Americans and promoting British soft power in a joint effort with Prince Harry on May 14, his party colleagues will be contemplating his latest gambit and mulling their next moves. What they decide in the small world of Westminster is likely to play out on a global scale.